Handbook of mathematical induction : : theory and applications / / David S. Gunderson.
"Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathe...
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Superior document: | Discrete mathematics and its applications |
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Place / Publishing House: | Boca Raton ;, London ;, NewYork : : CRC Press, Taylor & Francis Group,, [2010] 2010 |
Year of Publication: | 2010 |
Language: | English |
Series: | CRC Press series on discrete mathematics and its applications.
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Physical Description: | 1 online resource (xxv, 893 pages) :; illustrations. |
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Gunderson, David S., author. Handbook of mathematical induction : theory and applications / David S. Gunderson. Boca Raton ; London ; NewYork : CRC Press, Taylor & Francis Group, [2010] 2010 1 online resource (xxv, 893 pages) : illustrations. text txt rdacontent computer c rdamedia online resource cr rdacarrier Discrete mathematics and its applications Includes bibliographical references and indexes. What is mathematical induction? -- Foundations -- Variants of finite mathematical induction -- Inductive techniques applied to the infinite -- Paradoxes and sophisms from induction -- Empirical induction -- How to prove by induction -- The written MI proof -- Identities -- Inequalities -- Number theory -- Sequences -- Sets -- Logic and language -- Graphs -- Recursion and algorithms -- Games and recreations -- Relations and functions -- Linear and abstract algebra -- Geometry -- Ramsey theory -- Probability and statistics. "Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics. In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, transfinite induction, the axiom of choice, Zorn's lemma, empirical induction, and fallacies and induction. He also explains how to write inductive proofs. The next part contains more than 750 exercises that highlight the levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. Each self-contained chapter in this section includes the necessary definitions, theory, and notation and covers a range of theorems and problems, from fundamental to very specialized. The final part presents either solutions or hints to the exercises. Slightly longer than what is found in most texts, these solutions provide complete details for every step of the problem-solving process."--Publisher's description. Description based on print version record. Electronic reproduction. Ann Arbor, MI : ProQuest, 2018. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries. Proof theory. Induction (Mathematics) Logic, Symbolic and mathematical. Probabilities. Electronic books. Print version: Handbook of mathematical induction : theory and applications. Boca Raton ; London : New York : CRC Press, Taylor & Francis Group, c2010 xxv, 893 pages 9781420093643 (DLC) 2010029756 ProQuest (Firm) CRC Press series on discrete mathematics and its applications. https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=5379135 Click to View |
language |
English |
format |
eBook |
author |
Gunderson, David S., |
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Gunderson, David S., Handbook of mathematical induction : theory and applications / Discrete mathematics and its applications What is mathematical induction? -- Foundations -- Variants of finite mathematical induction -- Inductive techniques applied to the infinite -- Paradoxes and sophisms from induction -- Empirical induction -- How to prove by induction -- The written MI proof -- Identities -- Inequalities -- Number theory -- Sequences -- Sets -- Logic and language -- Graphs -- Recursion and algorithms -- Games and recreations -- Relations and functions -- Linear and abstract algebra -- Geometry -- Ramsey theory -- Probability and statistics. |
author_facet |
Gunderson, David S., |
author_variant |
d s g ds dsg |
author_role |
VerfasserIn |
author_sort |
Gunderson, David S., |
title |
Handbook of mathematical induction : theory and applications / |
title_sub |
theory and applications / |
title_full |
Handbook of mathematical induction : theory and applications / David S. Gunderson. |
title_fullStr |
Handbook of mathematical induction : theory and applications / David S. Gunderson. |
title_full_unstemmed |
Handbook of mathematical induction : theory and applications / David S. Gunderson. |
title_auth |
Handbook of mathematical induction : theory and applications / |
title_new |
Handbook of mathematical induction : |
title_sort |
handbook of mathematical induction : theory and applications / |
series |
Discrete mathematics and its applications |
series2 |
Discrete mathematics and its applications |
publisher |
CRC Press, Taylor & Francis Group, |
publishDate |
2010 |
physical |
1 online resource (xxv, 893 pages) : illustrations. |
contents |
What is mathematical induction? -- Foundations -- Variants of finite mathematical induction -- Inductive techniques applied to the infinite -- Paradoxes and sophisms from induction -- Empirical induction -- How to prove by induction -- The written MI proof -- Identities -- Inequalities -- Number theory -- Sequences -- Sets -- Logic and language -- Graphs -- Recursion and algorithms -- Games and recreations -- Relations and functions -- Linear and abstract algebra -- Geometry -- Ramsey theory -- Probability and statistics. |
isbn |
9781420093650 9781420093643 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA9 |
callnumber-sort |
QA 19.54 G86 42011 |
genre |
Electronic books. |
genre_facet |
Electronic books. |
url |
https://ebookcentral.proquest.com/lib/oeawat/detail.action?docID=5379135 |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
511 - General principles of mathematics |
dewey-full |
511.3/6 |
dewey-sort |
3511.3 16 |
dewey-raw |
511.3/6 |
dewey-search |
511.3/6 |
oclc_num |
1035519175 |
work_keys_str_mv |
AT gundersondavids handbookofmathematicalinductiontheoryandapplications |
status_str |
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ids_txt_mv |
(MiAaPQ)5005379135 (Au-PeEL)EBL5379135 (CaPaEBR)ebr11554475 (OCoLC)1035519175 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Discrete mathematics and its applications |
is_hierarchy_title |
Handbook of mathematical induction : theory and applications / |
container_title |
Discrete mathematics and its applications |
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fullrecord |
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